📖 比率分析练习

Financial Statement Analysis

I. Lesson Focus

This lesson consolidates all major ratio categories tested at CFA Level I: liquidity, solvency, profitability, activity (efficiency), and valuation ratios. Special emphasis is placed on DuPont decomposition of ROE, cash-flow quality red flags, and the integrated use of ratios to detect financial statement manipulation. Candidates must be able to calculate every ratio, interpret changes, and reconcile conflicting signals using real financial data.

II. The Problem

An equity analyst reviewing a manufacturing company’s three-year financial statements notices that the current ratio has been steadily rising, yet operating cash flow remains negative. Gross margin is improving while inventory turnover has collapsed. Investors want to know whether the firm is fundamentally sound or whether management is engaging in aggressive accounting. Systematic ratio analysis, combined with DuPont decomposition and cash-flow reconciliation, is required to reach a defensible conclusion—the exact skill CFA Level I examiners test repeatedly.

III. Core Framework and Classification of Ratios

Ratio analysis links different line items in the financial statements to reveal operating performance, financial position, and risk. CFA Level I organizes ratios into five functional groups:

1. Liquidity Ratios — measure ability to meet short-term obligations
2. Current Ratio = Current Assets / Current Liabilities
3. Quick Ratio = (Current Assets − Inventories) / Current Liabilities

4. Cash Ratio = (Cash + Cash Equivalents) / Current Liabilities

5. Solvency Ratios — measure long-term debt-servicing capacity

6. Debt-to-Asset Ratio = Total Liabilities / Total Assets
7. Equity Multiplier = Total Assets / Shareholders’ Equity

8. Interest Coverage = EBIT / Interest Expense

9. Profitability Ratios

10. Gross Profit Margin = Gross Profit / Revenue
11. Net Profit Margin = Net Income / Revenue
12. Return on Assets (ROA) = Net Income / Average Total Assets

13. Return on Equity (ROE) = Net Income / Average Shareholders’ Equity

14. Activity (Efficiency) Ratios

15. Inventory Turnover = Cost of Goods Sold / Average Inventory
16. Receivables Turnover = Revenue / Average Receivables
17. Total Asset Turnover = Revenue / Average Total Assets

18. Payables Turnover = Cost of Goods Sold / Average Payables

19. Market and Growth Ratios

20. Price-to-Earnings (P/E) = Market Price per Share / EPS
21. Price-to-Book (P/B) = Market Price per Share / Book Value per Share

IV. DuPont Analysis — The Heart of Ratio Analysis

DuPont analysis decomposes ROE into its fundamental drivers so analysts can determine why ROE changed and whether the change is sustainable.

Three-Factor DuPont Identity
$$ ROE = \text{Net Profit Margin} \times \text{Asset Turnover} \times \text{Equity Multiplier} $$
or
$$ ROE = \frac{\text{Net Income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Average Total Assets}} \times \frac{\text{Average Total Assets}}{\text{Average Equity}} $$

Five-Factor DuPont (extended version) further breaks EBIT margin and the tax burden:
$$ ROE = \left( \frac{\text{EBT}}{\text{EBIT}} \right) \times \left( \frac{\text{EBIT}}{\text{Sales}} \right) \times \left( \frac{\text{Sales}}{\text{Average Total Assets}} \right) \times \left( \frac{\text{Average Total Assets}}{\text{Average Equity}} \right) \times (1 - \text{Tax Rate}) $$

The analytical power of DuPont lies in its ability to separate margin, turnover, and leverage effects. An increase in ROE caused solely by higher leverage is usually viewed as riskier than an increase driven by improved margins or turnover.

V. Financial Reporting Quality Warning Signals

Analysts must watch for inconsistencies across ratios and the cash-flow statement:
- Rising current ratio accompanied by persistently negative operating cash flow often signals aggressive revenue recognition or deferred expense recognition.
- Improving gross margin with declining inventory turnover may indicate overstated inventory or cost capitalization.
- Receivables collection period materially longer than industry peers suggests channel stuffing or inadequate bad-debt provisions.
- Rising leverage coupled with a falling interest-coverage ratio indicates increasing financial risk.

Worked Cases

Worked Case 1: Liquidity and Activity Analysis

XYZ Corp. reports (in millions): Current assets = 480, Inventory = 160, Current liabilities = 240, Revenue = 1,200, COGS = 840, Average inventory = 140.

Calculations:
- Current Ratio = 480 / 240 = 2.0
- Quick Ratio = (480 − 160) / 240 = 1.33
- Inventory Turnover = 840 / 140 = 6.0 times
- Days of Inventory on Hand = 365 / 6.0 ≈ 60.8 days

Interpretation: Although the current ratio of 2.0 appears healthy, an industry benchmark of 35 days inventory on hand indicates severe inventory overhang and potential impairment risk.

Worked Case 2: DuPont Decomposition of ROE Change

ABC Corp. data:

2022: Net income = 80, Sales = 800, Avg. assets = 1,000, Avg. equity = 500 → ROE = 80 / 500 = 16.0%
Net margin = 10.0%, Asset turnover = 0.80, Equity multiplier = 2.0
DuPont check: 10% × 0.80 × 2.0 = 16.0%

2023: Net income = 96, Sales = 960, Avg. assets = 1,200, Avg. equity = 550 → ROE = 96 / 550 ≈ 17.45%
Net margin = 10.0%, Asset turnover = 0.80, Equity multiplier ≈ 2.182
DuPont check: 10% × 0.80 × 2.182 ≈ 17.45%

Conclusion: The entire ROE increase stems from higher financial leverage. Profitability and operational efficiency remained unchanged, implying higher risk.

Worked Case 3: Solvency and Profitability Cross-Check

DEF Corp.: EBIT = 1.5 m, Interest expense = 0.4 m, Net income = 0.82 m, Total assets = 12 m, Equity = 6.5 m.

Calculations:
- Interest Coverage = 1.5 / 0.4 = 3.75×
- ROA = 0.82 / 12 ≈ 6.83%
- ROE = 0.82 / 6.5 ≈ 12.62%
- Implied tax rate ≈ 26.4%

Interpretation: Coverage of 3.75× is marginal if the industry median exceeds 6×; earnings are sensitive to interest-rate increases.

Traps

Key Formulas

• Quick Ratio = (Current Assets − Inventory − Prepayments) / Current Liabilities
• DuPont: ROE = Net Margin × Asset Turnover × Equity Multiplier
• Cash Conversion Cycle = DIO + DSO − DPO
• Sustainable Growth Rate = ROE × (1 − Dividend Payout Ratio)
• Interest Coverage = EBIT / Interest Expense (safe > 1.5×)
• Equity Multiplier = 1 + Debt/Equity

Practice Questions

Q1. A company reports current assets of $400 m, inventory $120 m, prepayments $20 m, and current liabilities $250 m. Its quick ratio is closest to:
A. 1.04 B. 1.20 C. 1.60 D. 2.00

Q2. If a firm’s ROE rises from 12% to 15% while net profit margin and asset turnover remain unchanged, the most likely cause is:
A. Decreased equity multiplier B. Increased financial leverage C. Higher inventory turnover D. Lower gross margin

Q3. Which ratio best reflects short-term liquidity risk?
A. Interest coverage B. Quick ratio C. Total asset turnover D. P/E ratio

Q4. Revenue is $8,000 m and average receivables are $600 m. Receivables turnover is closest to:
A. 10.0× B. 13.33× C. 15.0× D. Cannot be calculated

Q5. In DuPont analysis, if heavy borrowing increases the equity multiplier while net margin falls, ROE will most likely:
A. Definitely rise B. Definitely fall C. Either rise or fall depending on magnitudes D. Remain unchanged

Q6. EBIT = $240 m, interest expense = $60 m, pre-tax income = $180 m, tax rate = 25%. Interest coverage ratio is:
A. 3.0 B. 4.0 C. 4.5 D. 6.0

Q7. Which situation most strongly suggests premature revenue recognition?
A. Sharply declining days sales outstanding B. Rising inventory turnover C. Operating cash flow materially lower than net income D. Continuously falling gross margin

Q8. If a firm’s cash ratio is well below industry average while its current ratio is above average, the most probable explanation is:
A. High inventory levels B. Excessive short-term debt C. Increased deferred revenue D. Aggressive capital expenditure

Answers

Takeaways

• Always benchmark ratios against industry peers, historical trends, and the cash-flow statement.
• DuPont analysis is the mandatory tool for explaining ROE changes; master the three-factor version cold.
• The quick ratio is more reliable than the current ratio in inventory-heavy industries.
• Averages (not ending balances) are required for ROA, ROE, and all turnover ratios unless the vignette states otherwise.
• Look for “ratio divergence”: rising margins with falling turnover, or rising earnings with negative operating cash flow—these are classic manipulation signals.
• Interest-coverage numerator must be EBIT; using net income is a frequent trap that costs points.